One of the government's key arguments for reforming public sector pensions crumbled when it was made clear that they are projected to become more affordable in the future, not less, as teachers staged the biggest school strikes since the 1980s over the plans.

The forecast that the cost of paying pensions to 6 million public sector workers will fall by £67bn over the next 50 years undermined David Cameron's claim earlier this week that the system could "go broke" if it is not reformed.

More than 2 million pupils missed classes as a group of four breakaway unions staged the first mass strikes against the coalition's austerity plans.

Thousands of parents were forced to take a day off work with nearly 6,000 schools closed and 5,000 partially closed. In total, half of schools were affected.

"Today's action across the country demonstrates the anger and distress that this government is causing teachers," Christine Blower, general secretary of the National Union of Teachers, said.

"Teachers are dedicated to the children and young people whom they teach. But they cannot stand back and see their pensions attacked when all the evidence shows that they are affordable and sustainable and that their costs are falling."

Ministers claimed a lower turnout in the civil service betrayed a lack of support for the unions' tactics. Downing Street said that just half of members of the PCS – the civil service union that has been at the forefront of the strikes – took part and that the impact was minimal.

"The figures speak for themselves," the prime minister's official spokesman said. Some rival unions also turned on the strikers accusing them of a "tactical error".

Warnings of chaos at airports, triggered by the UK Border Agency suggesting people should fly another day, failed to materialise. UKBA reported "minimal" impact on the estimated 500,000 passengers.

Thousands marched through central London where there were minor skirmishes between some protesters and the police. In total, 30 people were arrested.

Mark Serwotka, leader of the PCS, claimed that the strike was the biggest in their history. "It's a very, very clear signal to the government that they have been rumbled," he said.

"This is not about pensions, this is about making public sector workers pay for the economic problems, and we are determined to keep going until they change direction." He pointed out that the 100,000 was substantially in excess of the 48,500 who backed the strike in the ballot.

Serwotka accused the Cabinet Office minister, Francis Maude, who is leading the negotiations, of "floundering" when asked to justify earlier statements that pensions were becoming unaffordable.

Maude would only say that the Hutton report, on which the pension plans are based, had "very clearly" said that the status quo was not tenable. "You cannot continue to have more and more people in retirement being supported by fewer and fewer people in work," he said.

He later argued that public sector workers would have to justify the cost of their pensions as schools and hospitals were cutting their budgets.

The report by Lord Hutton, the former Labour work and pensions secretary who wrote the blueprint for the government's reforms, said that the cost of public sector pensions, as a proportion of GDP, was set to fall after peaking last year at 1.9% to 1.4% by 2059/60.

The prime minister's official spokesman dismissed the row. "People are getting caught up in a semantic debate," he said.

The Treasury later claimed that the graphs containing the figures included reforms the unions objected to, including a switch from CPI to RPI for up-rating pensions and the benefits of a "cap and share" scheme to cover extra costs of life expectancy changing. Without these factored in, the cost as a proportion of GDP would remain static at 1.8%.

Government ministers took to the airwaves highlighting the fact that the strikers had not been joined by the majority of unions.

Michael Gove, the education secretary, said: "Two particular teachers' unions thought that it would be a good idea in a way to pre-empt the completion of talks by going out on strike to demonstrate the strength of feeling. I think that's unnecessary."

Unions not involved suggested that early strikes had damaged their argument. "This was a tactical error. It's allowed the government to hone it's propaganda," one union boss said. "PCS was warned that this was the wrong time and could backfire. A lot of other unions will feel frustrated with PCS. Most unions will say today hasn't helped and wasn't very necessary."

Chris Keates, the general secretary of the NASUWT union, the only teaching union not to strike, said: "It is important to keep the high moral ground. That has been a key factor in our strategy. We're sticking with the negotiating and responding to what our members tell us."